ACMS Conference Proceedings 1977Copyright (c) 2023 Taylor University All rights reserved.
https://pillars.taylor.edu/acms-1977
Recent documents in ACMS Conference Proceedings 1977en-usTue, 25 Jul 2023 15:50:16 PDT3600Epistomology to Ontology
https://pillars.taylor.edu/acms-1977/25
https://pillars.taylor.edu/acms-1977/25Wed, 22 Jun 2022 14:33:15 PDT
This paper offers commentary on the various philosophical approaches to the foundations of mathematics and then indicates how these ideas have implications in consideration of the existence question.
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Charles R. HamptonRecent Parallels Between the Philosophy of Science and Mathematics
https://pillars.taylor.edu/acms-1977/11
https://pillars.taylor.edu/acms-1977/11Mon, 17 Jan 2022 13:35:09 PST
Following World War I European philosophy of science formed an alliance with mathematics culminating in an attitude of certainty and autonomy that rejected all non empirical claims to truth and purported to make all science presupposition less. The rise and fall of logical positivism has been one of the major themes of of twentieth century thought and illustrates the danger of placing too much emphasis on science and mathematics as an ideal for all knowledge. The restriction of rational inquiry to the modes of scientific verification and the processes of mathematical logic was far too confining for the containment of truth. Even after the rejection of logical positivism as a general epistemology on the ground that not all empirical knowledge was like scientific knowledge, it continued to survive as a philosophy of science and became the dominant influence on American science after World War II. Thus science became isolated from other realms of thought. This dichotomy has only recently been bridged by a more historically oriented approach. This paper discusses how the philosophies of science and mathematics have experienced a number of parallels in the development of these trends.
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Joseph SpradleyInfinity & Reality
https://pillars.taylor.edu/acms-1977/12
https://pillars.taylor.edu/acms-1977/12Mon, 17 Jan 2022 13:35:09 PST
This paper examines the topics of infinity and reality as relevant to the conference, proposing a possible relationship between the two in order to stimulate further discussions.
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John W. WarnerCurrent Work on Mathematical Truth
https://pillars.taylor.edu/acms-1977/9
https://pillars.taylor.edu/acms-1977/9Mon, 17 Jan 2022 13:35:08 PST
The overall aim of this paper is to serve as an introduction to the work currently being done on the topic of mathematical truth. It provides an overview of the major developments concerning mathematical truth and also evaluates those developments as potential contributions to mathematician’s understanding of the subject.
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Michael DetlefsenWanted: Christian Perspectives in the Philosophy of Mathematics
https://pillars.taylor.edu/acms-1977/10
https://pillars.taylor.edu/acms-1977/10Mon, 17 Jan 2022 13:35:08 PST
This paper describes the three types of theory about universals, beginning in each case with a classical historical formulation and moving to its restatement in recent analytic philosophy. It will then suggest ways in which Christian perspectives bear on theories of universals and so on mathematics.
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Arthur F. HolmesSkolem’s Paradox and the Predestination/Free-Will Discussion
https://pillars.taylor.edu/acms-1977/7
https://pillars.taylor.edu/acms-1977/7Mon, 17 Jan 2022 13:35:07 PST
The purpose of this paper is to show that both sides of the predestination/free-will discussion are admissible in a way that is more profound than simply the wave-particle duality of light. In wave-particle duality there are two competing physical models of reality which are contradictory. This paper will show that not a contradiction but a difference in viewpoint is the fundamental issue in the discussion of predestination and free will. A discussion of Skolem’s paradox is helpful in this demonstration.
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Gene B. ChaseA Brief Introduction to Gödel’s Theorems
https://pillars.taylor.edu/acms-1977/8
https://pillars.taylor.edu/acms-1977/8Mon, 17 Jan 2022 13:35:07 PST
Gödel’s two famous incompleteness theorems are results that have come up a number of times in the discussions at the 1977 ACMS conference. This paper provides a brief and relatively non-technical statement on these results and of their significance for the foundations of mathematics.
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Michael DetlefsenRecent Problems in the Foundationsof Mathematics
https://pillars.taylor.edu/acms-1977/6
https://pillars.taylor.edu/acms-1977/6Wed, 14 Jul 2021 13:44:10 PDT
This paper examines the foundational crises that have haunted twentieth-century mathematics, beginning with a brief review of the effects generated by Gauss, Lobachevsky, and Bolyai who each developed non-Euclidean parallel axiom. Though of mathematical interest in their own right, the significance of the new geometries was greatly magnified when it was discerned that they could be used to adequately model physical space, even to the extent that Einstein’s theory of relativity later employed as its model a non-Euclidean geometry developed by Riemann. The question that obviously presented itself was how could any given geometry be called true when it and others contradictory to it all could be interpreted so as to fit physical space?
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Terence H. PercianteA Christian Point of View
https://pillars.taylor.edu/acms-1977/5
https://pillars.taylor.edu/acms-1977/5Wed, 14 Jul 2021 13:44:07 PDT
Does the fact that you are a Christian affect the way that you teach mathematics? This paper seeks to answer the question, what contributions can a mathematics teacher in a Christian school make to the distinctive purpose of such a school?
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A. Wayne RobertsExistence in Mathematics
https://pillars.taylor.edu/acms-1977/4
https://pillars.taylor.edu/acms-1977/4Thu, 29 Apr 2021 11:41:39 PDT
Contemplation of the existence of mathematical entities for very apparent reasons generates a mental cycling of arguments dealing with the nature of mathematical truth, meaning in mathematics, and the obviously related question of which of these two problems should be solved first. The problem of the existence of mathematical entities dates from the first thoughts and ideas of a mathematical nature. The problem of existence in mathematics is fundamental to the domain of speculation and research on the foundations of mathematics. When we try to put ourselves in the place of those philosophers who first explored this problem we must realize that it sprang from the apparent or obvious discrepancy between the truths of mathematics and the entities to which these truths refer. The problem appears to be that the truths of mathematics belong to those elements of human knowledge to which we ascribe the highest degree of certainty; but we search vainly in the world of human experience, for entities which have properties described by these truths.
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Willis AlberdaThe Foundations of Mathematics and The Mathematics Curriculum
https://pillars.taylor.edu/acms-1977/3
https://pillars.taylor.edu/acms-1977/3Thu, 29 Apr 2021 11:41:35 PDT
In teaching the foundations of mathematics within the framework of a Christian college, and particularly that of a Christian liberal arts college, there are two groups of students which must be served. The first consisted of the non-mathematics majors—those non-scientifically oriented “general anything” students who, as a catalog might put it, are to receive “an introduction to and an appreciation of the history, foundations, culture and applications of mathematics.” The second group consists of the mathematics majors, and the few science majors who have not been frightened away by the calculus. The gulf between these two groups is sufficiently large, I believe, to indicate the use of two different strategies.
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Bayard BaylisTable of Contents (1977)
https://pillars.taylor.edu/acms-1977/2
https://pillars.taylor.edu/acms-1977/2Mon, 25 Jan 2021 13:35:46 PSTAssociation of Christians in the Mathematical SciencesIntroduction (1977)
https://pillars.taylor.edu/acms-1977/1
https://pillars.taylor.edu/acms-1977/1Mon, 25 Jan 2021 13:35:39 PSTRobert Brabenec